The lunar module was too
unstable to fly. It would have been impossible for it to hover
balanced on a thin column of thrust. Any movement by the astronauts
would have thrown it into an uncontrollable tumble.

This particular stability problem is as old as rocketry itself.
The conspiracists' insistence that it poses a special problem for the
lunar module is evidence of their lack of education and experience
with rocket science. In fact, every rocket must "balance" on
its "column" of thrust, whether it's going up or down. Or stated more
scientifically, the thrust vector must point very nearly through the
rocket's center of mass at all times in order to avoid unwanted
rotation of the vehicle.

In any rocket, wind buffeting can momentarily point the rocket in
the wrong direction. And the depletion of propellant causes a
constant shift in the center of mass. Any successful rocket must
therefore adjust its thrust vector as the center of mass shifts, and
be otherwise able to counteract rotations caused by external and internal
forces.

Over the centuries rocket scientists have used a number of
ingenious methods to do this.

Fig. 1 -The classic skyrocket uses a wooden stick to
provide an aerodynamic tail. As the rocket rotates, wind
pressure on the tail forces it back into straight flight.

The classic early skyrocket shown in Fig. 1 attaches the rocket
proper to a long thin stick. The stick would drag in the air behind
the rocket and help keep it on a straight course, much like the tail
fins on later rockets. By placing a large aerodynamic area
behind the rocket's center of gravity, and keeping in mind that
all rotations will be about the center of mass, the rocket designer
can arrange that wind pressure will push the back of the rocket back
into line behind the rocket's center of mass.

Dr. Robert Goddard's early rockets employed a different principle.
Fig. 2 shows his landmark 1926 liquid-fueled rocket. Fuel is the
heaviest part of any rocket, so Goddard placed it below the combustion
chamber and nozzle. The throat of the rocket exhaust is the center of
thrust, so if the center of mass (probably somewhere just above the
fuel tank) hangs below it, Goddard believed the rocket would stabilize
itself like a pendulum "suspended" beneath the rocket's thrust.

This turned out not to be the case; it doesn't matter whether the
center of thrust is above or below the center of mass. And since it's
impractical to put the fuel supply beneath the nozzle where hot
exhaust gas will strike it, Goddard returned to the traditional
fuel-on-top configuration and provided broad tail fins to allow for
aerodynamic stabilization.

This is passive stabilization -- designing a rocket so that the
act of tipping out of alignment will automatically result in a force
that brings it back into line. Active forms of stabilization were
also considered, especially for rotational forces that exceeded the
ability of passive features to correct it. This is extremely
important for military rockets and other rockets that must fly very
precisely to their destinations.

Early rocket scientists realized that if they could tell when the
rocket was tipping and apply a correction quickly enough, they could
stop the tip before it became a fatal tumble. To detect tipping, you
need some reference against which to measure the orientation of the
rocket. Then you need some way to rotate the rocket back to its
intended orientation. And all this has to work quickly enough to
catch rotation before it becomes too serious.

The active forms of stabilization are very important to the lunar
module's design because there is no air to push against fins and
realign the rocket if its axis points in a different direction than
its flight path. Aerodynamic stabilization was not an option. Hence
the lunar module designers turned to a sophisticated,
computer-controlled active guidance system.

The lunar module had two stages, one used for the descent and
another for the return to lunar orbit and rendezvous with the command
module. The descent stage engine had a throttle to control the amount
of thrust. The engine was also gimbaled (Fig. 3d) and could swivel
up to 6° in either side-to-side direction. And of course it had
a set of RCS thrusters (Fig. 3e).

Fig. 5 - Schematic of the primary guidance and stabilization
system of the lunar module. A completely separate system can
take over in the event this one fails.
Legible version (141 KB).
(Northrop Grumman)

Most importantly, the lunar module had not one, but two
separate computer-based guidance systems. One was built around the
same hardware as the command module's guidance computer. The other
was much simpler and could only be used to abort the landing and/or
return to orbit. The main guidance computer (Fig. 5) was responsible
for checking the lunar module's attitude several times a second and
adjusting the engine gimbal to keep it balanced. The conspiracist's
assertion that an astronaut shifting his weight in the cockpit would
throw the vehicle off balance is entirely unfounded. In fact, if an
astronaut took a step to one side and altered the LM's center of mass,
the computer would be making the necessary corrections even before the
astronaut had finished taking the step.

In fact, the lunar module was essentially "fly-by-wire". The
pilot's hand controller was not usually directly wired into the engine
gimbal or RCS system, although it could be. Most often it simply told
the computer which direction the LM should move -- left, right,
forward, or backwards. The computer adjusted the gimbal angle to
produce the desired lateral motion. The pilot was not required to
manually maintain the LM's balance.

The problem of shifting centers of mass in rockets had been solved
by the 1940s. It's simply ridiculous to suppose that the lunar module
provides any special difficulty. In fact, we'll see below that it's
actually easier to keep the lunar module from tumbling than it
is to control a common cylindrical rocket.

But the lunar module
ascent stage engine could not gimbal. It was fixed in place. It was
therefore too unstable to fly.

First, the same computer that controlled the descent also
controlled the ascent. The same RCS that used to help control the
descent performed all of the attitude control for the ascent. As the
off-axis thrust caused the ascent stage to rotate, the RCS jets fired
to counter the rotation and return it to the correct attitude. This
is why the films of the LM ascent seem to show a periodic sway or
oscillation: the RCS "fought" the off-axis ascent engine.

Second, the LM ascent stage is a much more inherently stable
spacecraft than a cylindrical rocket from an inertial point of view.
(Keep in mind a rocket that flies through air can use the air to make
it overall very stable.) Fig. 6 shows a front view of the LM ascent
stage and the location of the people and things that affect the
vehicle's center of mass.

The ascent engine is mounted inside the spacecraft, not attached
to the bottom of it. This places the center of mass very near the
center of thrust, limiting the rotational effect of off-axis thrust.
In fact, during the first few seconds of the ascent the centers of
thrust and mass are very close together.

The most massive component of any spacecraft like the lunar module
is fuel. The fuel tanks are mounted as low as possible, and carefully
balanced left-to-right. (Oxidizer is denser than fuel and therefore
the fuel tank is positioned farther outboard.) Though not shown in
Fig. 6, the RCS fuel tanks are mounted behind the astronauts, helping
to balance the spacecraft front-to-back.

The astronauts are inboard of the fuel tanks and are considerably
less massive. Their motion is further restricted by the cramped
cabin. Thus the idea that the movements of the astronauts would spell
doom for a stable ascent completely ignores the fact that the much
more massive fuel is mounted farther outboard where it has a greater
effect due to its steady depletion. In fact, the massive fuel tanks
would actually damp, or lessen, the effects of the astronauts'
movements in the same way the long pole carried by a tightrope walker
increases his balance.

Note also the extreme outboard position of the RCS thrusters.
They are mounted on outriggers to increase their moment arm
(rotational force). For small rotations, the thrusters are fired in
"pulse mode" which uses very short bursts.

ANATOMY OF A
TUMBLE

The theory of balancing on a rocket on its thrust (neglecting
aerodynamic effects) is pretty simple. In most spacecraft the center
of thrust (c.t.) and center of mass (c.m.) are arranged as in Fig. 7a.
The center of mass is the point around which the spacecraft will
naturally rotate, and the point at which the force of gravity (if any)
will act (Fig. 7b). The center of thrust is the point at which the
force of the engine is applied (Fig. 7c), generally the throat of the
engine.

Fig. 7 - Vector diagram of off-axis thrust. (a) The
relationship between the center of mass, c.m., and the center of
thrust, c.t., in the typical rocket. (b) Gravity acts downward at
the center of mass. (c) A well-trimmed engine points its thrust
vector toward the center of mass. (d) If the thrust is off-axis, a
portion of the thrust applies torque at the center of thrust.

If the rocket engine is correctly trimmed, the engine will be
gimballed so that the thrust vector (T in Fig. 7c) points along the
line joining the centers of thrust and mass. But if the center of
mass changes -- e.g., an astronaut moves or the fuel sloshes in the
tanks -- the thrust vector T will no longer point in the right
direction.

Fig. 8 - The effect of distance from the center of mass
(c.m.) on torque. (a) A long distance applies more torque than a
short distance (b).

When this happens, T can be thought of ("decomposed" in
geometrical terms) as a combination of a vector Tp that
points along the correct axis and continues to provide thrust, and
Tr which acts perpendicular to the axis (Fig. 7d). It is
Tr which concerns us, because it will apply a torque, or
rotational force to the spacecraft. If uncorrected, the force
continues to act and will increase the rate at which the spacecraft
rotates. In Fig. 7d the force will rotate the spacecraft clockwise.
Gravity, G, always acts downward. When the c.m./c.t. line becomes
horizontal, the engine thrust will no longer oppose gravity at all.
The component of T that acts propulsively along this axis,
Tp, will no longer have any upward component itself.
(Tp is the linear component, Tr is the
rotational component.)

Let's briefly consider only the rotational component, Tr.
If the center of thrust is far away from the center of mass,
Tr acts with more leverage to rotate the spacecraft
(Fig. 8a). If we move the engine closer to the center of mass
(Fig. 8b), we reduce the leverage and therefore reduce the torque, or
twisting force, that is applied to the spacecraft. The plumber's
trick of slipping a length of pipe on the handle of the wrench in
order to break loose a rusted joint is an application of this
principle.

Fig. 9 - Cutaway view of the V2 rocket. The center of
mass (c.m.) probably lies close to the center of the fuel tank
assembly, offset aft by the mass of the engine. The center of
thrust (c.t.) is at the throat of the engine. (Drawing
courtesy V2Rocket.com)

The traditional rocket (Fig. 9) has a center of mass located far up
its length. The center of thrust will always be at the aft end. This
means that the traditional rocket behaves like Fig. 8a where torque is
amplified. Consequently off-axis thrust in a traditional rocket
design is a more serious problem than it would be in the lunar module
(Fig. 6). The center of thrust is at the astronauts knee level. The
visual center of mass (our estimate of the center of mass based on the
geometrical center of the cross section) is at the astronauts' chest
level. Thus the c.m./c.t. line is only two or three feet (ca. one
meter) long. Considered proportionally to the mass of the vehicle,
off-axis thrust in the lunar module will exert far less torque in the
lunar module than in the V2.

But the main source of mass in the ascent stage is the fuel tanks,
whose centers are located far below the visual center of mass. This
would offset the center of mass downward. While computing the actual
center of mass is a very complicated and tedious process, we can be
sure that the center of mass does not lie any higher than the
astronauts' chest, and likely lies far lower -- perhaps even below the
center of thrust.

How can you say the
lunar module ascent stage is a more inherently stable design? A
cylindrical rocket's moment of inertia is greater than that of the
roughly spherical ascent stage. That means a cylindrical spacecraft
will resist torque more than a spherical one, and is therefore a
better design.

This is a valid observation according to physics, but its effects
are overshadowed by the position of the LM ascent engine and the
resulting substantial reduction in moment.

JUST A
MOMENT

"Moment of inertia" is the rotational equivalent of mass.
Newton's laws of motion clearly say that a mass will resist attempts
to move it (or stop it if it's already moving), and the resistance is
proportional to the mass of the object. Similarly, a mass will resist
attempts to rotate it, and the resistance is proportional to a
combination of the object's mass and shape. Long, skinny objects
resist changes in rotation more than spherical objects of the same
mass. This is intuitively obvious to those who have ever carried
lumber. You shoulder a plank, balancing its center of mass over your
shoulder. But as you turn your body you find that the plank doesn't
want to rotate with it, and once it's turning it doesn't want to stop.
The art of baton twirling is based on the high moment of inertia of
such an object.

Consider two hypothetical spaceships of identical mass, containing
identical volumes. One is spherical, while the other is cylindrical.
The length of the cylinder is five times its diameter (an arbitrary
choice). The radius of the resulting cylinder will be about half the
radius of the spherical spacecraft.

In this case the cylinder will have more than five times the
moment of inertia as the sphere. In other words, it would take five
times as much torque to produce the equivalent rotation rate in the
cylinder as in the sphere, even though they have identical mass.

But as we discussed above, the answer lies in how close to the
center of mass our engine is placed. In the cylindrical spacecraft
(i.e., a rocket), the engine is placed at one end of the cylinder. If
we place the sphere's engine anywhere on the surface of the sphere,
the engine in the cylinder will produce about 2.5 times more torque
because it's so far away from the center of mass. Factoring in moment
of inertia, the rotational acceleration of the sphere will be about
twice that of the cylinder for the same amount of off-axis thrust.

If, as in the case of the LM ascent stage, the engine is placed
inside the sphere, closer to the center of mass, the amount of torque
produced by off-axis thrust is greatly reduced. In fact, we would
have to move it inward by only about half the radius in order to
equalize the situation, and if we placed it at 1/3 the radius we will
have achieved a more stable design than the cylinder, even though the
sphere doesn't resist rotation as well as the cylinder.

The best evidence for the stability of the LM design is empirical.
Find a yardstick or meter stick. Try to balance it vertically on end
on your hand. You probably won't be able to do it for very long. But
balance it horizontally, using the graduations as a guide in finding
the center of mass. You should be able to do this easily, and may
even be able to move your hand around without upsetting the stick.
The mass and moment of inertia are identical in these cases, but you
apply less torque by off-axis support when the stick is horizontal.